Optimizing quantitative trait locus (QTL) mapping experiments requires a generalized measure of marker informativeness because variable information is obtained from different marker systems, marker distribution and pedigree types. Such a measure can be derived from the concept of Shannon entropy, a central concept in information theory. Here we introduce entropy-based founder informativeness(EFI), a new measure of information content generalized across pedigrees, maps, marker systems and mating configurations. We derived equations for inbred- and outbred-derived mapping populations. Mathematical properties of EFI include enhanced sensitivity to mapping population type and extension to any number of founders. To illustrate the use of EFI, we compared experimental designs for QTL mapping for three examples: (i) different marker systems for an F2 pedigree, (ii) different marker densities and sampling sizes for a BC1 pedigree and (iii) a comparison of haplotypic versus zygotic analyses of an outbred pedigree. As an a priori generalized measure of information content, EFI does not require phenotypic data for optimizing experimental designs for QTL mapping.

There has recently been increased interest in the use of Markov Chain Monte Carlo (MCMC)-based Bayesian methods for estimating genetic maps. The advantage of these methods is that they can deal accurately with missing data and genotyping errors. Here we present an extension of the previous methods that makes the Bayesian method applicable to large data sets. We present an extensive simulation study examining the statistical properties of the method and comparing it with the likelihood method implemented in Mapmaker. We show that the Maximum A Posteriori (MAP) estimator of the genetic distances, corresponding to the maximum likelihood estimator, performs better than estimators based on the posterior expectation. We also show that while the performance is similar between Mapmaker and the MCMC-based method in the absence of genotyping errors, the MCMC-based method has a distinct advantage in the presence of genotyping errors. A similar advantage of the Bayesian method was not observed for missing data. We also re-analyse a recently published set of data from the eggplant and show that the use of the MCMC-based method leads to smaller estimates of genetic distances.

Data from an F2 cross between breeds of livestock are typically analysed by least squares line-cross or half-sib models to detect quantitative trait loci (QTL) that differ between or segregate within breeds. These models can also be combined to increase power to detect QTL, while maintaining the computational efficiency of least squares. Tests between models allow QTL to be characterized into those that are fixed (LC QTL), or segregating at similar (HS QTL) or different (CB QTL) frequencies in parental breeds. To evaluate power of the combined model, data wih various differences in QTL allele frequencies (FD) between parental breeds were simulated. Use of all models increased power to detect QTL. The line-cross model was the most powerful model to detect QTL for FD>0·6. The combined and half-sib models had similar power for FD<0·4. The proportion of detected QTL declared as LC QTL decreased with FD. The opposite was observed for HS QTL. The proportion of CB QTL decreased as FD deviated from 0·5. Accuracy of map position tended to be greatest for CB QTL. Models were applied to a cross of Berkshire and Yorkshire pig breeds and revealed 160 (40) QTL at the 5% chromosome (genome)-wise level for the 39 growth, carcass composition and quality traits, of which 72, 54, and 34 were declared as LC, HS and CB QTL. Fourteen CB QTL were detected only by the combined model. Thus, the combined model can increase power to detect QTL and mapping accuracy and enable characterization of QTL that segregate within breeds.